Performance of an improved one-way error reconciliation protocol based on key redistribution

In data post-processing for quantum key distribution, it is essential to have a highly efficient error reconciliation protocol. Based on the key redistribution scheme, we analyze a one-way error reconciliation protocol by data simulation. The relationship between the error correction capability and the key generation efficiency of three kinds of Hamming code are demonstrated. The simulation results indicate that when the initial error rates are (0,1.5%], (1.5,4%], and (4,11%], using the Hamming (31,26), (15,11), and (7,4) codes to correct the error, respectively, the key generation rate will be maximized. Based on this, we propose a modified one-way error reconciliation protocol which employs a mixed Hamming code concatenation scheme. The error correction capability and key generation rate are verified through data simulation. Using the parameters of the posterior distribution based on the tested data, a simple method for estimating the bit error rate (BER) with a given confidence interval is estimated. The simulation results show that when the initial bit error rate is 10.00%, after 7 rounds of error correction, the error bits are eliminated completely, and the key generation rate is 10.36%; the BER expectation is 2.96 × 10^-10, and when the confidence is 95% the corresponding BER upper limit is 2.17 × 10^-9. By comparison, for the single (7,4) Hamming code error reconciliation scheme at a confidence of 95%, the key generation rate is only 6.09%, while the BER expectation is 5.92 × 10^-9, with a BER upper limit of 4.34 × 10^-8. Hence, our improved protocol is much better than the original one.